Answer
$74$
Work Step by Step
The last given equation has, on the RHS,
a product of factors $(x-2)\cdot q(x)+r(x)$
Since $x-2$ is zero when $x=2$,
the RHS equals $74$ when $x=2.$
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Alternatively, we can interpret the second equation as
$f(x)=g(x)\cdot q(x)+r$,
obtained by the division algorithm - special case.
Since we divided $f(x) $ with $(x-2)$, we can apply the Remainder theorem:
$f(2)=r=74$
